\newpage is a low level command on which
\cleardoublepage are built upon. It ends the current paragraph (if not issued between paragraphs), fills the current page with white space and starts a new page.
\clearpage does something more, as it also flushes the float queues, producing pages of floats if necessary, then starts a new page.
\cleardoublepage is the same as
\clearpage, but it also checks the number of the last ejected page; if the number is odd and
twosided typesetting is in force, it fills another blank page so the new page to start on will be again odd-numbered.
\pagebreak is quite different from
\newpage and its siblings described above.
If issued inside a paragraph, it will force a page break after the line in which it happens to fall when the paragraph is eventually typeset. It also issues no white space filling command, so the last line on the page will be at the bottom margin when
\flushbottom is in force (for instance with
book or generally with
If issued between paragraphs, it will force a page break without filling.
This command is useful in the last stage of document production: one can force a page break at a convenient spot for improving the typesetting of the next page. Clearly, the text should be in definitive form for this to be effective.
\pagebreak has an optional argument, which can be a number among 0, 1, 2, 3, 4. Issuing
\pagebreak is the same as
\pagebreak just marks a point where a page break is possible (after the line it falls in). The other numbers mark a greater “desirability” of a page break.